1. Field of the Invention
The present invention relates to soft or inferential sensors and, more particularly, to inferential sensors that are developed using a three-dimensional Pareto-front genetic programming technique.
2. Description of Related Art
Industrial processes are often monitored and controlled by measuring various process parameters. Such process parameters may include, for example, temperature, pressure, flow rates, etc., depending on the industrial process. Some of the relevant process parameters may be relatively easy to measure, e.g., using hardware sensors, while the process is on-line. Other process parameters, however, may be difficult to measure under normal operating conditions. Inferential sensors or soft sensors have been used to infer such difficult-to-measure process parameters (output variables) based on easily-measured process parameters (input variables).
In a typical approach for developing an inferential sensor for a given process, historical data is collected for a broad range of process conditions. Using this historical data, various techniques may then be used to develop an empirical model that can predict the desired output variable based on the available input variables. Linear regression is one technique that could potentially be used. In practice, however, linear regression has only limited applicability because the majority of industrial processes are nonlinear, especially in the chemical industry.
Neural network models have been used to model nonlinear industrial processes. However, neural network models are often associated with a number of different problems. First, neural network models can experience high sensitivity toward process changes. This, in turn, may create a need for frequent model re-development and re-adjustment.
Second, neural network models often exhibit poor performance outside of the range used for model development. In other words, once a neural network model has been trained with a given range of values, the neural network model may be unable to extrapolate well outside of that range. The inability to extrapolate could have disastrous consequences for certain industrial processes, especially in the chemical industry.
Third, a neural network model may be viewed as a “black box,” in that the neural network may make predictions without making clear the mechanism for prediction. Thus, neural network models can be difficult to interpret.
Fourth, neural network models can be difficult to implement and support. They may require specialized software and specialized training.
Accordingly, there is a need for other ways of developing inferential sensors that can infer difficult-to-measure process parameters based on easily-measured process parameters.